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Q1)A ladder of a fire truck is elevated to an angle of 60 degrees and extended to a length of 70 feet. if the base of the ladder is 7 fet above the ground, how many feet above the ground does the ladder reach? a) 35 b) 42 c) 35 \sqrt{3} d) 7+ 35\sqrt{3} e) 7+42\sqrt{3}

Q2) the price of lunch for 15 people was $207.00, including a 15% gratuity for service. What was the average price per person EXCLUDING the gratuity? a)11.73 b)12 c)13.8 d)14 e)15.87

Q3) for any psitive integer n, the sum fo the first n positive integers equals [n(n+1)]/2. what si the sum of all the even integers betwen 99 and 301? a) 10,100 b) 20,200 c) 22,650 d) 40,000 e) 45,150

Q4)Last year the price per share of stock X increased by k percent and the earnings per share of stock X increased by m percent, where k is greater than m. By what percent is the ratio of price per share to the earnings per share increase, in terms of k and m? a) k/m b) k-m c) [100(k-m)]/ 100+k d) [100(k-m)]/[100+m] e) [100(k-m)/(100+k+m)

Q5) of the 300 subjects who participated in an experiment using virtual reality therapy to reduce their fear of heights, 40% experienced sweaty palms, 30% experienced vomiting, and 75% experienced dizziness. If all the subjects experienced at least one of these effects, and 35 % of the subjects experienced exactly two of these effects, how may of the subjects experienced only one of these effects? a)105 b)125 c)130 d)180 e)195

Q6) if m>0 and x is m percent of y, then in terms of m, y is what percent of x? a)100m b)1/(100m) c) 1/m d) 10/m e) 10,000/m

Q7) Seven pieces if rope have an average of length of 68 cmand median length of 84 cm. if the length f the longest piece of rope is 14 cm more than 4 times the length of the shortest piece of rope, what si maximum possible length , in cm, of the longest piece of rope? a)82 b)118 c)120 d)134 e)152

Q8) [0.99999999/1.0001]- [0.99999991/1.0003]= a) 10^-8 b) 3(10^-8) c) 3 (10^-4) d) 2(10^-4) e) 10^-4

Q9) List T consists of 30 positive decimals, none of which is an integer, and the sum of 30 decimals is S. the estimated sum of the 30 decimals, E is defined as follows. Each decimal in T whose tenths digit is even is rounded up to the nearest integer, and each decimal in T whose tenths digit is odd is rounded down to the nearest integer; E is the sum of the resulting integers. If 1/3 of the decimals in T have a tenths digit that is even, which of the following is a possible value of E-S? 1. -16 2. 6 3.10

A) 1 only B) 1 and 2 only C) 1 and 3 only D) 2 and 3 only E) 1,2 and 3

Last edited by bb on 13 Apr 2013, 00:18, edited 2 times in total.

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08 Apr 2013, 09:05

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That's a lot of questions !

Q1)A ladder of a fire truck is elevated to an angle of 60 degrees and extended to a length of 70 feet. if the base of the ladder is 7 fet above the ground, how many feet above the ground does the ladder reach?

The ladder forms a 30 60 90, triangle which has dimentions 1x \(\sqrt{3}\) 2, the hip is \(70=2x\) so \(x=35\), the H of the triangle is \(35\sqrt{3}\), but the ladder is 7 feet from the ground => it reaches \(7+35\sqrt{2}\)

IMO D
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Q3) for any psitive integer n, the sum fo the first n positive integers equals [n(n+1)]/2. what si the sum of all the even integers betwen 99 and 301?

100 ... 200 ... 300 Between 200 and 100 there are 200/2-100/2+1=51 even integers Between 300 and 200 there are 300/2-200/2+1=51 even integers But we counted 200 twice, so tot even entegers = \(51+51-1=101.\) As you can see their mean is 200 So tot sum is\(200*101=20200\) IMO B
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Quote:

Q3) for any psitive integer n, the sum fo the first n positive integers equals [n(n+1)]/2. what si the sum of all the even integers betwen 99 and 301? a) 10,100 b) 20,200 c) 22,650 d) 40,000 e) 45,150

Sum of all even integers is Avg. * count of numbers in series 99 - 301

Avg = first + last / 2 = 100 + 300 / 2 = 200 count of numbers in the series = 300 - 100 / 2 + 1 = 101

Sum = 200 * 101 = 20200. Answer is B

//Kudos please, if the above explanation is good
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Q5) of the 300 subjects who participated in an experiment using virtual reality therapy to reduce their fear of heights, 40% experienced sweaty palms, 30% experienced vomiting, and 75% experienced dizziness. If all the subjects experienced at least one of these effects, and 35 % of the subjects experienced exactly two of these effects, how may of the subjects experienced only one of these effects?

Use the formula : Tot = S+V+D-(two)+2(three) = 100

300 = 120 + 90 + 225 - 105 - 2*(three) so 15 had all three

To see the number of subjects with 1 effect: S+V+D-2*two-3*three = 435 - 210 - 45 = 180

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Q3) for any psitive integer n, the sum fo the first n positive integers equals [n(n+1)]/2. what si the sum of all the even integers betwen 99 and 301? a) 10,100 b) 20,200 c) 22,650 d) 40,000 e) 45,150

No of even terms between 99 and 301-->(300-100)/2 +1 = 101. Thus the sum = \(101/2 * (100+300)\) = 200*101 = 20200 B.
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Quote:

Q5) of the 300 subjects who participated in an experiment using virtual reality therapy to reduce their fear of heights, 40% experienced sweaty palms, 30% experienced vomiting, and 75% experienced dizziness. If all the subjects experienced at least one of these effects, and 35 % of the subjects experienced exactly two of these effects, how may of the subjects experienced only one of these effects?

Let x represent subjects who experienced only sweaty palms Let y represent subjects who experienced only vomiting Let z represent subjects who experienced only dizziness Let a represent subjects who experienced only sweaty palms and dizziness Let b represent subjects who experienced only sweaty palms and vomiting Let c represent subjects who experienced only vomiting and dizziness Let d represent subjects who experienced vomiting, sweaty palms, and dizziness

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Q7. Mean of 7 wood pieces = 68 therefore total length of 7 pieces = 68 * 7 = 476 cms

Median of 7 pieces = 84 To have the 7th piece of maximum length we must have 4th, 5th, 6th piece = median length of 84 and 1st, 2nd and 3rd piece = smallest wood length.

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Q2) the price of lunch for 15 people was $207.00, including a 15% gratuity for service. What was the average price per person EXCLUDING the gratuity? a)11.73 b)12 c)13.8 d)14 e)15.87

Here the word EXCLUDING is used. So 0.15 * 207=$31.05 Therefore,207-31.05=$175.95

So the average cost per person=175.75/15=11.73 So ans should be (A) IMO.

gmatclubot

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